When to Push Ads : Optimal Mobile Ad Campaign Strategy under Markov Customer Dynamics

Problem Definition: We investigate a seller's optimal advertising campaign strategy targeting customers who interact with the seller over time. We model customers' engagement as a continuous-time Markov chain with two states, active and inactive. While in the active state, customers make purchases according to a Poisson process, with each purchase yielding a specific reward; in contrast, customers in the inactive state make no purchases. The seller aims to optimize the expected average profit by promptly activating customers through costly advertising campaigns contingent on their purchase histories.Methodology/Results: For the unconstrained problem, we demonstrate the optimality of a threshold policy based on the elapsed time since the last purchase or ad campaign. When confronted with a budget constraint on the overall ad cost, we suggest first solving a static problem and then implementing a separate threshold policy for each customer with a specified budget. We establish the asymptotic optimality of this policy and show that the asymptotic loss order is $O(1/\sqrt{T})$. Furthermore, we explore two extensions: strategic customer reactions and probabilistic customer activation. Despite these additional complexities, our main findings remain robust, yielding additional insights into these scenarios.Managerial Implication: Our findings reveal that the seller tends to push ads earlier to customers with high purchase rates and low recapture rates (i.e., low transition rates from an inactive state to an active state). Surprisingly, we also observe that the seller should push ads earlier to customers with intermediate churn rates (i.e., intermediate transition rates from an active state to an inactive state) compared to those with small or large churn rates. Moreover, we propose an easy-to-implement and asymptotically optimal policy under budget constraints